A B C If: $ BC = 5x + 6$, $ AB = 3x + 9$, and $ AC = 55$, Find $BC$.
Solution: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {3x + 9} + {5x + 6} = {55}$ Combine like terms: $ 8x + 15 = {55}$ Subtract $15$ from both sides: $ 8x = 40$ Divide both sides by $8$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $BC$ $ BC = 5({5}) + 6$ Simplify: $ {BC = 25 + 6}$ Simplify to find ${BC}$ : $ {BC = 31}$